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%I #7 Apr 11 2021 23:40:40
%S 0,0,0,0,0,0,0,2,1,1,0,6,0,2,5,11,0,13,0,19,12,6,0,43,15,9,24,40,0,52,
%T 0,55,30,16,45,136,0,20,44,141,0,110,0,105,160,30,0,258,69,141,75,149,
%U 0,216,124,298,96,49,0,509,0,56,346,362,176,295,0,260,140
%N Number of partitions of n into 4 parts s,t,u,v such that (s+t+u+v) | s*t*u*v.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (1 - ceiling(i*j*k*(n-i-j-k)/n) + floor(i*j*k*(n-i-j-k)/n)).
%e a(8) = 2; [1,1,2,4] and [2,2,2,2], where (1+1+2+4) | 1*1*2*4 and (2+2+2+2) | 2*2*2*2.
%e a(9) = 1; [1,2,3,3], where (1+2+3+3) | 1*2*3*3.
%t Table[Sum[Sum[Sum[(1 - Ceiling[i*j*k*(n - i - j - k)/n] + Floor[i*j*k*(n - i - j - k)/n]), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
%Y Cf. A343270.
%K nonn
%O 1,8
%A _Wesley Ivan Hurt_, Apr 11 2021
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